4B.3.3 Testing the product moment correlation coefficient Quiz: Pearson Edexcel Further Maths, Unit 20

The 20 questions

1. Which null hypothesis is used to test whether a product moment correlation coefficient is zero?

   • H0: sample r = 1
   • H0: rho = 0
   • H0: mu_x = mu_y
   • H0: rho = 1

2. What underlying population distribution is required for product moment correlation critical values?

   • Uniform
   • Poisson
   • Binomial
   • Bivariate normal

3. For the test statistic t = r sqrt(n - 2) / sqrt(1 - r^2), what are the degrees of freedom?

   • n - 2
   • n
   • n + 2
   • n - 1

4. Which test is suitable for correlation when data are not from a bivariate normal distribution?

   • Product moment test
   • Spearman's test
   • Chi-squared test
   • Two-sample t-test

5. What happens to the product moment correlation coefficient if a constant is added to every x value?

   • Multiplied by constant
   • Unchanged
   • Increased by constant
   • Squared

6. What is the alternative hypothesis for a one-tailed test expecting a positive correlation?

   • rho < 0
   • rho != 0
   • rho = 0
   • rho > 0

7. When the p-value is less than the significance level in a correlation test, what is the conclusion?

   • Reject H0
   • Accept H0
   • Accept H1
   • Do not reject H0

8. A sample of n = 12 pairs has r = 0.6. What is the test statistic t, to 2 decimal places?

   • 3.46
   • 1.58
   • 0.60
   • 2.37

9. With n = 12, r = 0.6, and critical value 2.228, what is the conclusion at the 5% level?

   • Inconclusive
   • Accept H1
   • Reject H0
   • Accept H0

10. With n = 20, r = 0.3, and critical value 1.734, is the result significant at the 5% one-tailed level?

    • Cannot tell
    • Always
    • No
    • Yes

11. A sample of n = 10 pairs has r = -0.7. What is the test statistic t, to 2 decimal places?

    • 2.77
    • -0.91
    • -1.98
    • -2.77

12. A sample of n = 17 pairs has r = 0.45. What is the test statistic t, to 2 decimal places?

    • 1.74
    • 0.45
    • 1.95
    • 2.13

13. A sample of n = 8 pairs has r = 0.8. What is the test statistic t, to 2 decimal places?

    • 2.45
    • 4.80
    • 1.33
    • 3.27

14. With n = 6, r = 0.9, and critical value 4.604, is H0 rejected at the 1% level?

    • Always
    • No
    • Maybe
    • Yes

15. A sample of n = 27 pairs has r = 0.4. What is the test statistic t, to 2 decimal places?

    • 1.09
    • 2.06
    • 0.40
    • 2.18

16. Which assumption must hold for the product moment correlation test statistic to be valid?

    • Uniform
    • Bivariate normal
    • Binomial
    • Poisson

17. With r = 0.45, n = 12, and critical value 1.812, what is the conclusion for H1: rho > 0?

    • Reject H0
    • Not significant
    • Accept H1
    • Significant

18. What primary effect can a single extreme outlier have on the product moment correlation coefficient?

    • Always decrease r
    • Inflate or deflate r
    • No effect on r
    • Always increase r

19. A test gives t = 3.0 with critical values 2.306 at 5% and 3.355 at 1%. What is the conclusion?

    • Not significant
    • Significant at 5% only
    • Significant at 1% only
    • Significant at both

20. For a fixed sample correlation r = 0.3, which sample size yields the larger test statistic t?

    • n = 30
    • n = 20
    • n = 100
    • n = 10

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